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Philosophia Mathematica Advance Access originally published online on July 1, 2006
Philosophia Mathematica 2006 14(3):318-337; doi:10.1093/philmat/nkl005
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Philosophia Mathematica (III), Vol. 14 No. 3 © The Author [2006]. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oxfordjournals.org

Burgess's ‘Scientific’ Arguments for the Existence of Mathematical Objects{dagger}

Chihara Charles*

* Department of Philosophy, University of California Berkeley Berkeley, California 94720-2390, U. S. A. charles1{at}berkeley.edu

This paper addresses John Burgess's answer to the ‘Benacerraf Problem’: How could we come justifiably to believe anything implying that there are numbers, given that it does not make sense to ascribe location or causal powers to numbers? Burgess responds that we should look at how mathematicians come to accept:

There are prime numbers greater than 1010

That, according to Burgess, is how one can come justifiably to believe something implying that there are numbers. This paper investigates what lies behind Burgess's answer and ends up as a rebuttal to Burgess's reasoning.


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